\section{结论}\label{conclusion}
%This paper has proposed an optimised TLM iteration method for finite element simulation of nonlinear axisymmetrical magnetostatic field. A new equivalent circuit of FEM equation  and parallel TLM iteration process are introduced. The electromagnetic force of a  permanent magnet actuator is calculated through FEM and TLM iteration. Compared with measured data, the results show the accuracy of TLM. Moreover, we have presented its excellent performance with the scheme of an N-R preconditioner and parallel triangle system solver. The TLM's calculation time is more than 10 times faster than the conventional Newton-Raphson solver. In the future, we may further study the application of TLM in 3-D problems and other physical fields, like mechanics and heat.
这篇文章提出了一种改进的传输线迭代方法来进行轴对称非线性静磁场的有限元求解，其中介绍了有限元方程的等效电路模型的建立和并行的TLM迭代过程。通过TLM迭代和有限元方法，文中计算了含永磁制动器的电磁力。与实测的电磁力数据对比，结果表明TLM的计算满足精度要求。同时，我们还通过牛顿预处理器和并行的三角求解器来提高迭代的计算速度。TLM的计算时间跟传统的牛顿迭代法相比快了十倍多。在以后的研究中，我们会进一步的研究TLM方法在三维问题和其他物理场当中的应用，例如热场、结构力场等。





